New York Democratic mayoral hopeful Bill de Blasio and his family celebrate a strong primary showing at his campaign headquarters Tuesday night. (AP Photo/Kathy Willens)

New York Democrats have voted in big numbers for the contender who just days ago was dismissed by outgoing Mayor Mike Bloomberg as “a very populist, very left-wing guy.”

Bloomberg thought that was a negative assessment.

But Bill de Blasio did, indeed, run as a very populist, at least reasonably left-wing guy who promised to deliver “the bold progressive change this city needs.”

That worked for Democratic primary voters. With more than 98 percent of the votes counted, de Blasio was winning a high enough percentage of the vote—just over 40 percent—to possibly avoid a runoff election with the next strongest Democratic finisher.

The margins were such that a runoff might still be required: de Blasio had 40.2 percent of the votes as of Wednesday morning with thousands of paper ballots yet to be counted. Even when the initial count is completed, a recount could still give a runoff slot to second-place finisher William Thompson, who trailed de Blasio by almost 100,000 votes.

The wide lead that de Blasio ran up in Tuesday’s voting was a remarkable development for a candidate who just a few weeks ago was running fourth in the polls.

The de Blasio surge signaled an embrace of a populist politics that the candidate, at his packed election night party in Brooklyn, described as an “unapologetically progressive alternative to the Bloomberg era.”

Like most of the other contenders in a crowded field of Democratic candidates, the city’s elected Public Advocate embraced a socially-liberal agenda on issues such as marriage equality. But de Blasio did not stop there. He ran on a platform that proposed to increase taxes on the rich in order to raise $500 billion to fund education and community initiatives.

Beyond the specifics of his tax plans, de Blasio promised not to “nibble around the edges of the inequities facing our city.”

That was a specific rejection of the approach advanced for more than a decade by Bloomberg, who New York Times columnist Frank Bruni acknowledged on Monday has “worshiped at the altar of Wall Street.”

The closing message from de Blasio said as much:

“For twelve long years, New York City has lived by Mayor Bloomberg’s false choices. We couldn’t ask the wealthy to pay a little more in taxes to help our children get a great education. We couldn’t keep our streets safe without infringing on the rights of millions of New Yorkers—mostly young men of color. And our neighborhoods couldn’t thrive if affordable housing was the priority,” the candidate declared.

The conclusion from de Blasio was blunt and unapologetic: “For twelve long years, we’ve had a Mayor who doesn’t understand this, and his false choices have created the Tale of Two Cities we’re living today.”

Bloomberg dismissed that kind of talk as “class warfare.”

He also suggested that de Blasio was running a “racist” race by campaigning with his African-American wife and their children.

Both charges from the outgoing mayor were absurd, and even Bloomberg allies dismissed his intervention in the contest as “unfortunate.”

Even as Bloomberg and his allies attacked, de Blasio’s poll numbers rose. The candidate who had trailed through much of the race became a frontrunner.

He remained so on election night, celebrating that 40.2 percent vote total—14 percent more than the next most popular Democratic contender, former New York Comptroller Thompson.

If the margin holds, de Blasio will not need to run the October 1 runoff race with Thompson, who split key unions endorsements with the Public Advocate.

The results may take several days, perhaps even weeks, to sort out.

Even if he is secures the Democratic nod, De Blasio will still have to compete on November 5 with Republican nominee Joe Lhota, an ally of former Republican Mayor Rudy Giuliani.

Bloomberg, the billionaire businessman who was elected initially as a Republican and then became an independent, will almost certainly position himself at Lhota’s side. And the campaign could yet by an ugly one, as the city’s economic, political and media establishment seeks to derail de Blasio and his big ideas for addressing income inequality.

But Bloomberg and his crew have had a hard time blocking de Blasio.

The mayor made little secret of his enthusiasm for New York City Council President Christine Quinn in the Democratic primary. But on Tuesday, she collected just 15 percent of the vote—running 25 points behind de Blasio.

John Nichols explores Mike Bloomberg’s freak-out over Bill de Blasio’s tax populist campaign.